While I agree that research hidden behind paywalls is annoying, to disallow reference to anything that is not available for free is to disallow some of the best research available. I realize we are on a website here, but we live in the real world, and in the real world scientists submit papers to journals based on the topicality and reputation of the journal mostly without regard to whether the paper will be made freely available.
In my opinion, citing papers in academic journals should be done by way of PubMed. This is a central repository run by the NIH where pretty much everything related to the bio-medical field is indexed. There is also an abstract for nearly all primary data. The abstract summarizes the point of the trial, the basic methodology, and the findings. The availability of the full text on PubMed generally falls into three categories:
Available in full from the journal: Here is an example of a paper I recently cited. You’ll notice that on that page there is a link to free full text from the journal. That’s because it’s an old article, and NEJM makes old things available.
Available in full from Pubmed Central: Here is a (randomly chosen) example. Some journals make all articles immediately available this way. Others choose a few articles (based on mostly mysterious criteria) to publish immediately in Pubmed Central, and others get added later. If you see a Pubmed Central button like the one below, click on that preferentially rather than the journal button. The latter will lead to a paywall in many instances.
- Available only via paywall or library access: For newer papers, you may see something like this. This links to the journal itself, where you are prompted to pay or log in. If you are unable to do either, you can’t see the full text. However, note that the abstract is still available. An abstract usually contains sections like Background, Methods, Results, and Conclusions. If an SE answer is using the paper to make a point consistent with its main findings, the abstract will provide confirmation of the data cited on SE as well as context.1 Also, if you click on “author information” in PubMed you can usually find an email address (see below).
If you want more details than those provided in the abstract, there are several choices:
- Ask the answerer. I’ll go on record as more than happy to provide additional info if queried in comments, or to add it to the post if people find that lacking.
Email the corresponding author.2 This works remarkably well. Just be respectful, explain why you’re interested and your lack of access to an academic library, and ask politely for a copy of the article or more specifics about the data than available in the abstract.3 Most of the time, the author will just send you a pdf. Emailing this sort of request to a corresponding author is not going to surprise or offend (most of) them.4
Look on academia.edu. Many authors upload their papers here.
Please see also the biology.SE meta post on this topic. More recently, a related question was asked on meta.SE.
Addendum in response to another answer:
If an answer has citations and references that are behind a pay wall then it means that other users, the person asking the question especially, have no way of verifying the information presented and that in a way is worse then an answer with no citations.
In my opinion, an answer that links to a resource that is not peer-reviewed and does not tell me how they arrived at their conclusions is less valuable than a resource that has been peer-reviewed, is published in a respectable journal, and has an abstract available on PubMed.
1. From the linked paper about abstracts: «Thus, for the vast majority of readers, the paper does not exist beyond its abstract. For the referees, and the few readers who wish to read beyond the abstract, the abstract sets the tone for the rest of the paper.»
2. If not available in the author information, most university-associated academics have emails that are easily found with a google search or via the university affiliation found in PubMed.
3. In addition to what I mentioned above, that sort of email should include the full title of the paper, the name of the journal in which it was published, and the year of publication. If you really like health.SE, you could also include a link to the site where you saw their paper referenced. :-)
4. Please do not upload PDFs of articles that are not made freely available by the journal. Whether you access them through a library or are sent them by an author, they are yours for personal use only.